Method and apparatus for measuring the time delay between signals

Abstract

A system for determining the delay between first and second signals includes apparatus for characterizing each signal and apparatus responsive to corresponding portions of the first and second characterizations for providing an estimate of the delay of the second signal relative to the first. In a preferred embodiment the characterizer dissects the signal into a plurality of separate components each having a different frequency. A cross-characterizer determines the time delay between corresponding components of the two characterizations and derives a weight for each determined delay. A cross-characterization combiner forms a weighted sum of the determined component delays which becomes the discriminated delay between the two signals.

What is claimed is: 
     
       1. A signal processing system for measuring the time delay between first and second signals, said system comprising: means for receiving said first and second signals; and   means for comparing said first signal to said second signal to determine the time delay of said second signal relative to said first signal comprising: means responsive to said first and second signals for dissecting them individually into respective first and second sets of components, each component having a power level, and a primary frequency range, each component in said first set having a different primary frequency range and having a corresponding component in said second set having the same primary frequency range;   means responsive to said corresponding components of said first and second sets for generating a weighted time delay of each component in said second set relative to its corresponding component in said first set; and   means for combining said weighted time delays to provide a measure of the time delay of said second signal relative to said first signal.     
     
     
       2. The system recited in claim 1 wherein: said means for receiving comprises first means for receiving said first signal and second means for receiving said second signal at a different location than said first means; and   said system further comprises means responsive to said measure of the time delay for determining the location of a common source of said first and second signals.   
     
     
       3. The signal processing system recited in claim 1 wherein: said means for dissecting comprises: means for taking a series of amplitude samples of each of said first and second signals and for converting each of said samples to a corresponding digital value;   means responsive to said digital values for Fourier transforming (1) a first set of said digital values derived from said first signal and (2) a second time related set of said digital values derived from said second signal to provide, respectively, first and second sets of Fourier transform data which include power and phase data at corresponding frequencies of said first and second sets; and     said means for generating is responsive to the frequency, phases and powers of corresponding components of said first and second sets of Fourier transform data.   
     
     
       4. The signal processing system recited in claim 3 wherein: said means for generating, in determining the time delay for a given pair of corresponding components, is responsive to their phases and their frequency; and   said means for generating, in deriving the weight associated with the time delay determination for the given pair, is responsive to the powers and the frequency of said corresponding components.   
     
     
       5. The signal processing system recited in claim 3 wherein said means for dissecting further includes means for processing with a window function, which reduces the magnitude of early and late samples of a set, (1) a set of said digital values from said first signal to provide said first set of digital values transformed by said means for transforming and (2) a time related set of said digital values from said second signal to provide said second set of digital values transformed by said means for transforming. 
     
     
       6. The signal processing system recited in claim 1 wherein said means for generating comprises: means for determining the time delay between said corresponding components and deriving a weight associated with each of said determined time delays; and   said means for combining is responsive to said determined time delays and their associated weights for producing said measure of the time delay of said second signal relative to said first signal.   
     
     
       7. The signal processing system recited in claim 6 wherein said means for determining and deriving is responsive to the frequency, phases and powers of said corresponding components for providing a determined time delay which is a function of said frequency and phases and an associated weight which is a function of said frequency and said powers. 
     
     
       8. The signal processing system recited in claim 7 wherein said means for determining and deriving comprises: means for providing said determined time delay for the components at a given freuqency with a value equal to the phase of said second component minus the phase of said first component divided by their frequency.   
     
     
       9. The signal processing system recited in claim 8 wherein said means for determining and deriving further comprises: means for providing said associated weight for each of said determined time delays with a value equal to twice the square of the frequency of the components to which said determined time delay applies times the product of the powers of those components divided by the sum of said powers.   
     
     
       10. A method of measuring the time delay between first and second signals which are susceptible to noise corruption, said method comprising the steps of: providing said first and second signals; and   comparing said first and second signals to determine the time delay of said second signal relative to said first signal by: dissecting said first signal into H frequency components and said second signal into H corresponding components at the same frequencies;   determining from corresponding first signal and second signal components i, for each integer value of i, i≦i≦H, both a time delay Δt i  of said second signal component i relative to said first signal component i and an associated weight (W i ) for that delay, said associated weight W i  having a value which depends on the noise corruption of said components i; and   combining said determined time delays Δt i  and their associated weights W i  to produce a weighted combination thereof as the value (Δt) of the measurement of the time delay of said second signal relative to said first signal, whereby said value Δt has a noise induced uncertainty which is less than it would be if said determined time delays Δt i  were combined without weighting.     
     
     
       11. The method recited in claim 10 wherein said combining step comprises: 
     
     
       multiplying each of said time delays Δt i  by its associated weight W i  to provide individual weighted time delays W i  Δt i  ; adding said individual weighted time delays together;   adding said individual weights W i  together;   dividing the sum of said weighted time delays by the sum of said weights; and   providing the result of said division as the measured value (Δt) of said time delay of said second signal relative to said first signal.   
     
     
       12. The method recited in claim 10 wherein said first and second signals are audio bandwidth signals derived respectively from first and second radio signals and said measured time delay is the difference in the time of arrival of said first and second radio signals. 
     
     
       13. The method recited in claim 10 wherein the time delay of said second signal relative to said first signal encodes transmitted data and said method further comprises: decoding said measured time delay value into a corresponding transmitted data value.   
     
     
       14. The method recited in claim 10 wherein said first and second signals are received respectively at first and second known, spaced apart locations and said method further comprises the step of: determining from said measured time delay value a set of possible locations of a common source of said first and second signals.   
     
     
       15. The method recited in claim 10 wherein said dissecting step comprises: sampling the amplitude of each of said signals at a rate commensurate with the bandwidth of said signals;   converting the amplitudes of said samples to digital values; and   Fourier transforming a set of 2H samples from said first signal and a time related set of said samples from said second signal to provide first signal transform data and second signal transform data, respectively, said transform data comprising said H frequency components.   
     
     
       16. The method recited in claim 15 wherein said first and second signals are audio bandwidth signals derived respectively from first and second radio signals and said measured time delay is the delay of said second radio signal relative to said first radio signal. 
     
     
       17. The method recited in claim 15 wherein said determining step comprises: for each frequency magnitude |f i  | in said Fourier transform data calculating the phase (φ 1i ) and power (S 1i ) of said first transform data and the phase (φ 2i ) and power (S 2i ) of said second transform data; and   for each frequency magnitude determining a time delay ##EQU9## where the differnece (φ 2i  -φ 1i ) is taken modulo 2π and determining a weight ##EQU10##   
     
     
       18. The method recited in claim 17 further comprising: determining a delay uncertainty σ 2  equal to ##EQU11## providing from a time sequence of J measurements of Δt (Δt j ,1≦j≦J) a refined measurement Δt of the delay of said second signal relative to said first signal, said refined measurement Δt having a smaller uncertainty than any of said Δt j  on which it is based.   
     
     
       19. A method of measuring the time delay between first and second analog signals, said method comprising the steps of: receiving said first and second analog signals; and   comparing said first analog signal to said second analog signal to determine said time delay between said first analog signal and said second analog signal by: sampling the amplitude of each of said analog signals at a rate commensurate with the bandwidth of said analog signals;   converting the amplitudes of said samples to digital values,   Fourier transforming a set of 2H samples from said first signal and a time related set of said samples from said second signal to provide first signal transform data and second signal transform data, respectively;   extracting the first transform data phase (φ 1i ) and power (S 1i ) and the second transform data phase (φ 2i ) and power (S 2i ) for each frequency magnitude |f i  | in said Fourier transform data;   for each frequency magnitude determining a time delay ##EQU12## where the difference (φ 2i  -φ 1i ) is taken modulo 2π and determining a delay weight ##EQU13##  and generating from said delays Δt i  and said weights W i  a measured value Δt of the time delay ##EQU14##     
     
     
       20. The method recited in claim 19 wherein said first and second analog signals are audio bandwidth signals derived respectively from first and second radio signals and said measured time delay is the time delay of said second radio signal relative to said first radio signal. 
     
     
       21. The method recited in claim 19 further comprising low pass filtering said received signals to remove components having frequencies above a threshold value prior to performing said sampling step.